| 000 -LEADER |
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| fixed length control field |
04657nam a2200709 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
6812532 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20200413152900.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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| fixed length control field |
m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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| fixed length control field |
cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
110219s2011 caua foab 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781608456147 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781608456130 (pbk.) |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.2200/S00327ED1V01Y201101MAS009 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(CaBNVSL)gtp00546204 |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)707877354 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
CaBNVSL |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA311 |
| Item number |
.K725 2011 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
515.42 |
| Edition number |
22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Krantz, Steven G. |
| Fuller form of name |
(Steven George), |
| Dates associated with a name |
1951- |
| 245 14 - TITLE STATEMENT |
|---|
| Title |
The integral |
| Medium |
[electronic resource] : |
| Remainder of title |
a crux for analysis / |
| Statement of responsibility, etc. |
Steven G. Krantz. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : |
| Name of publisher, distributor, etc. |
Morgan & Claypool, |
| Date of publication, distribution, etc. |
c2011. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 electronic text (xii, 93 p.) : |
| Other physical details |
ill., digital file. |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
# 9 |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
System requirements: Adobe Acrobat Reader. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Series from website. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (p. 87) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
1. Introduction -- What is an integral -- What is the Riemann integral -- What is the Riemann integral good for -- What is the Riemann integral not good for -- What is the Lebesgue integral -- What is the Lebesgue integral good for -- What is the Lebesgue not good for -- Exercises -- |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
2. The Riemann integral -- The definition -- Properties of the Riemann integral -- Characterization of Riemann integrability -- The fundamental theorem of calculus -- Numerical techniques of integration -- Introduction -- The method of rectangles -- The trapezoidal rule -- Simpson's rule -- Integration by parts -- Exercises -- |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
3. The Lebesgue integral -- Elementary measure theory -- Measurable sets -- The Lebesgue integral -- Three big theorems about the Lebesgue integral -- The Lebesgue spaces LP -- The Riesz representation theorem -- Product integration: Fubini's theorem -- Three principles of Littlewood -- Differentiation of integrals: covering lemmas and the Lebesgue theorem -- Basic ideas -- The maximal function -- The concept of convergence in measure -- Functions of bounded variation and absolute continuity -- Exercises -- |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
4. Comparison of the Riemann and Lebesgue integrals -- Any Riemann integrable function is Lebesgue integrable -- Exercises -- |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
5. Other theories of the integral -- The Daniell integral -- The Riemann-Stieltjes integral -- The Henstock-Kurzweil integral -- Hausdorff measure -- Haar measure -- The fundamental theorem -- Exercises -- |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Bibliography -- Author's biography -- Index. |
| 506 1# - RESTRICTIONS ON ACCESS NOTE |
|---|
| Terms governing access |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Compendex |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
|---|
| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Title from PDF t.p. (viewed on February 19, 2011). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Integral theorems. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Riemann integral. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Lebesgue integral. |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Riemann integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Lebesgue integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Henstock integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Daniell integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Stieltjes integral |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Limiting processes |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Inequalities |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Measure |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Measurable function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Lebesgue theorems |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| International Standard Book Number |
9781608456130 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis digital library of engineering and computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
# 9. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
http://ieeexplore.ieee.org/servlet/opac?bknumber=6812532 |
